Pragmatic trellis coded modulation (PTCM) employs primary and secondary modulation schemes. A first set of information bits being communicated is processed by the primary modulation scheme, and a second set of communicated information bits is processed by the secondary modulation scheme. Differential encoding may optionally be applied independently to the first and second sets of information bits to help a receiving decoder resolve rotational ambiguities. The secondary modulation scheme encodes the second set of information bits, which is optionally differentially encoded, with a strong error detection and correction code, such as the well known K=7, rate 1/2 "Viterbi" convolutional code (i.e., Viterbi encoding). The primary modulation scheme need not encode its subset of the information bits, other than the optional differential encoding. The resulting first and second sets of bits are then concurrently PSK or APSK mapped to generate quadrature components of a transmit signal.
The symbol data are conveyed through the phase (PSK) or amplitude and phase (APSK) relationships between the quadrature components of the transmit signal. The PSK or APSK mapping causes the phase constellation to be perturbed more by the primary modulation than by the secondary modulation.
PTCM has become popular because it allows a single convolutional encoder and decoder to achieve respectable coding gains for a wide range of bandwidth efficiencies (e.g., 1-6 b/s/Hz) and a wide range of higher order coding applications, such as 8-PSK, 16-PSK, 16-QAM, 32-QAM, etc. For lower order coding applications, such as QPSK or BPSK, PTCM offers no advantage because quadrature, complex communication signals provide two independent dimensions (i.e., I and Q) per unit baud interval with which to convey two or fewer symbols per unit interval.
APSK modulation achieves performance improvements over an otherwise equivalently ordered PSK modulation. A prior art sixteen phase-point rectilinear APSK (sixteen R-APSK) constellation 10 is shown in FIG. 1. Constellation 10 and other R-APSK modulations are conventionally referred to as quadrature amplitude modulation (QAM), but will be referred to herein using the generic term "R-APSK" to distinguish them from polar APSK (P-APSK) modulations, discussed below.
R-APSK constellations represent a special class of constellations where one set of symbols is conveyed independently of another set of symbols. In sixteen R-APSK (i.e., 16-QAM), two symbols are communicated using I-axis constellation perturbations and two symbols are communicated using Q-axis constellation perturbations. Since the I and Q axes are orthogonal, the two sets of symbols have no influence over one another.
PTCM has been adapted to R-APSK constellations with moderate success. Typically, one primary modulation symbol and one secondary modulation symbol are conveyed by perturbations about each of the I and Q axes. Unfortunately, conventional R-APSK constellations do not achieve rotationally invariant communication systems without accepting a tremendous degradation in performance (e.g., 4 dB). Without rotational invariance, the duration required for a decoder to achieve synchronization is much longer than with rotational invariance. When rotational invariance is sacrificed, conventional R-APSK constellations achieve acceptable performance, but performance is still not optimized.
FIG. 1 denotes a primary sub-constellation 12 included in the exemplary sixteen R-APSK constellation 10. Each primary sub-constellation 12 shares a common data value for the second set of information bits being communicated (i.e., the secondary modulation). Those skilled in the art will appreciate that constellation 10 actually includes four primary sub-constellations 12. FIG. 1 further denotes a single minimum secondary sub-constellation Euclidean distance 14 and a single minimum primary sub-constellation Euclidean distance 16 for the sixteen R-APSK example. Minimum secondary distance 14 is the smallest distance between phase points in constellation 10. Minimum primary distance 16 is the smallest distance between phase points in any given primary sub-constellation 12.
The value of these minimum distances has a large influence on respective secondary modulation and primary modulation performance. One reason R-APSK communication systems do not demonstrate better performance is believed to be that these distances result from discrete, independent I, Q values which dictate the positions of the phase points in constellation 10. For example, constellation 10 is achieved when phase points have I and Q coordinates consisting of all sixteen combinations of .+-.1 and .+-.3, scaled by a factor of 1/(3.sqroot.2). Minimum secondary distance 14 is 2/(3.sqroot.2), and minimum primary distance 16 is 4/(3.sqroot.2). As a result, the performance of primary modulation is not balanced with that of secondary modulation unless signal-to-noise ratio is held at a single specific value, and overall performance suffers.
Furthermore, conventional applications of PTCM to R-APSK constellations provide an excessive number of phase points at the respective minimum distances from other phase points. For the sixteen R-APSK example depicted in FIG. 1, four minimum primary sub-constellation Euclidean distances 16 exist for each of the four primary sub-constellations 12, resulting in a total of 16 minimum primary sub-constellation Euclidean distances 16 in constellation 10. This large number of minimum primary sub-constellation Euclidean distances 16 causes primary modulation performance to suffer. Likewise, for the sixteen R-APSK example depicted in FIG. 1, twenty-four minimum secondary sub-constellation Euclidean distances 14 exist in constellation 10. These twenty four minimum secondary sub-constellation Euclidean distances 14 operate in combination with the strength of a particular convolutional code to greatly influence secondary modulation performance.
Moreover, R-APSK constellations are particularly undesirably when used on peak power limited channels, such as characterize satellite communications. As illustrated by FIG. 1 for a specific sixteen R-APSK constellation, phase points reside in three concentric rings 18. Peak transmitter power is required to transmit phase points on the outer ring 18'. In random data, only 1/4 of the data are transmitted at this peak power. Accordingly, the peak power capability that must be provided in the transmitter is used to transmit only 1/4 of the data, resulting in an inefficient use of the peak power capability. In general, R-APSK constellations require an excessive number of phase points rings 18 for a given number of phase points in the constellation, and this excessive number of rings 18 causes an inefficient use of transmitter power so that an undesirably low amount of power is transmitted per bit.
Moreover, transmitter amplifiers introduce AM-AM and AM-PM distortions in the signals they amplify. AM-AM distortions characterize non-linear amplitude variations in an amplifier output signal which occur as a function of input amplitude but are not explained by amplifier gain. AM-PM distortions characterize phase variations in an amplifier output signal which occur as a function of input amplitude. The use of an excessive number of rings 18 in R-APSK for a given number of phase points requires transmitter amplifiers to operate at an excessive number of input amplitude states and causes an excessive amount of AM-AM and AM-PM distortions.
In theory, P-APSK constellations should have superior characteristics to R-APSK constellations, particularly in peak power limited channels. P-APSK constellations can be arranged so that a greater percentage of random data is transmitted using the peak power to achieve transmitter amplifier utilization efficiency. In addition, AM-AM and AM-PM distortions can theoretically be reduced if fewer rings are used to implement a phase constellation when compared to a R-APSK constellation having an equivalent number of phase points.
Unfortunately, conventional P-APSK constellations are not adapted to PTCM communication systems. Accordingly, such constellations have been proposed in either uncoded or in fully coded applications. Uncoded applications apply no convolutional coding to the communicated information bits, and fully coded applications apply convolutional coding to all communicated information bits. Uncoded applications are highly undesirable because they demonstrate significantly degraded performance when compared with equivalent pragmatic or fully coded applications. Fully coded applications are undesirable because they require the use of different convolutional encoders and decoders for different modulation orders.